MathDB

Let

\mathcal{R}

be the region consisting of the set of points in the coordinate plane that satisfy both |8 \minus{} x| \plus{} y \le 10 and 3y \minus{} x \ge 15. When

\mathcal{R}

is revolved around the line whose equation is 3y \minus{} x \equal{} 15, the volume of the resulting solid is

\frac {m\pi}{n\sqrt {p}}

, where

m

n

, and

p

are positive integers,

m

and

n

are relatively prime, and

p

is not divisible by the square of any prime. Find m \plus{} n \plus{} p.

Problem Statement